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Dynamical optimal transport problems (DOTPs) can be naturally interpreted as optimal control problems (OCPs) in the space of probability measures. This perspective opens the door to applying tools from optimal control theory to tackle challenges in optimal transport, particularly in high-dimensional settings. In this talk, I will present recent work on formulating and solving DOTPs through the lens of optimal control. The goal is to provide new insights and methodologies that mitigate the curse of dimensionality often encountered in DOTPs. In particular, we revisit ideas from dual optimal control theory developed prior to 1990s to derive novel dual formulations of DOTPs. These formulations offer alternative computational pathways and theoretical interpretations that may enhance both the analysis and numerical solution of dynamic optimal transport problems.

Bio: Dongjun Wu is currently a postdoctoral researcher at Lund University, Sweden. He obtained a double-PhD degree from University of Paris-Saclay and Harbin Institute of Technology in 2022. His research focuses on the intersection of optimization and control, with a particular interest in optimal control of large-scale systems and optimal transport.